A binary sequence may have a prescribed fraction p of ‘1’s. A special case occurs when p=0.5, wherein a codebook and its codewords are considered to be a balanced codebook with balanced codewords. Otherwise, the codebook and its codewords are considered to be an unbalanced codebook with unbalanced codewords.
Generally, in information theory, the channel capacity (i.e., the highest possible throughput that may be reliably communicated over a given channel) may be achieved only if a codebook used has an optimal input distribution. While the channel capacity concept has been known for 60 years, most of the codes that are used in digital communications systems are binary linear codes, which necessarily have Bernoulli (0.5) composition. That is, most of the codewords of binary linear codes have approximately half ‘1’s and half ‘0’s.
The use of binary linear codes limits the capacity-approaching possibility of channel codes to a small number of channel types, such as additive white Gaussian noise channels or binary symmetric channels. For channels with an optimal input composition other than Bernoulli (0.5), there may be very limited success in finding effective coding and decoding algorithms. Therefore, effective ways to generate error correction channel codes with good distance properties, i.e., good error correction capability given a prescribed composition, may extend performance success in channel coding theory to a wider range of channel types.